Only a one-to-one function can have an inverse function. Any one-to-one relationship (e.g. \(y = {x^3}\) or \(y = \ln x\)) or many-to-one relationship (e.g. \(y = {x^2}\) or \(y = \sin x\)) is a function. However, if we tried to find the inverse of a many-to-one function, we would obtain a one-to-many relationship which is not a function. Therefore, only a one-to-one function can have an inverse function.Use the interactive Geogebra applet...